It is known to use vibrating meters to measure mass flow and other information of materials flowing through a pipeline. One particular type of vibrating meter is a vibrating Coriolis flow meter as disclosed in U.S. Pat. No. 4,491,025 issued to J. E. Smith, et al. of Jan. 1, 1985 and Re. 31,450 to J. E. Smith of Feb. 11, 1982. These vibrating meters have one or more fluid tubes. Each fluid tube configuration in a Coriolis mass flow meter has a set of natural vibration modes, which may be of a simple bending, torsional, radial, lateral, or coupled type. Each fluid tube is driven to oscillate at resonance in one of these natural modes. The vibration modes are generally affected by the combined mass, stiffness, and damping characteristics of the containing fluid tube and the material contained therein. Therefore, the mass, stiffness, and damping are typically determined during an initial calibration of the vibrating meter using well-known techniques. Material flows into the flow meter from a connected pipeline on the inlet side of the vibrating meter. The material is then directed through the fluid tube or fluid tubes and exits the flow meter to a pipeline connected on the outlet side.
A driver applies a force to the one or more fluid tubes. The force causes the one or more fluid tubes to oscillate. When there is no material flowing through the flow meter, all points along a fluid tube oscillate with an identical phase. As a material begins to flow through the fluid tubes, Coriolis accelerations cause each point along the fluid tubes to have a different phase with respect to other points along the fluid tubes. The phase on the inlet side of the fluid tube lags the driver, while the phase on the outlet side leads the driver. Sensors are placed at two different points on the fluid tube to produce sinusoidal signals representative of the motion of the fluid tube at the two points. A phase difference of the two signals received from the sensors is calculated in units of time.
The time difference between the two sensor signals is proportional to the mass flow rate of the material flowing through the fluid tube or fluid tubes. The mass flow rate of the material is determined by multiplying the time difference by a flow calibration factor. The flow calibration factor is dependent upon material properties, tube geometry, and cross sectional properties of the fluid tube. One of the major characteristics of the fluid tube that affects the flow calibration factor is the fluid tube's stiffness. Prior to installation of the flow meter into a pipeline, the flow calibration factor is determined by a calibration process. In the calibration process, a fluid is passed through the fluid tube at a given flow rate and the proportion between the time difference and the flow rate is calculated. The fluid tube's stiffness and damping characteristics are also determined during the calibration process as is generally known in the art.
One advantage of a Coriolis flow meter is that the accuracy of the measured mass flow rate is not affected by wear of moving components in the flow meter, for example no sliding of gears, etc. The flow rate is determined by multiplying the time difference between two points on the fluid tube and the flow calibration factor. The only input is the sinusoidal signals from the sensors indicating the oscillation of two points on the fluid tube. The time difference is calculated from the sinusoidal signals. There are no moving components in the vibrating fluid tube. The flow calibration factor is proportional to the material and cross sectional properties of the fluid tube. Therefore, the measurement of the phase difference and the flow calibration factor are not affected by wear of moving components in the flow meter.
However, it is a problem that the cross sectional properties of a fluid tube can change during use of vibrating meters. The changes in the material and cross sectional properties of the fluid tube can be caused by erosion, corrosion, and coating of the fluid tube by material flowing through the fluid tube.
Although prior art attempts have been made to provide a method for detecting a change in the cross-sectional areas of the fluid tubes in situ, these attempts are relatively limited. For example, U.S. Pat. No. 6,092,409, assigned on its face to the present applicants, discloses a system for detecting changes in the cross-sectional areas of the fluid tubes based on a change in the period of oscillation of the fluid tubes. A problem with this approach is that the method requires a known density to be flowing within the fluid tubes during the measurement. Without a known fluid flowing through the fluid tubes, the change in the period of oscillation may be due to a change in the cross-sectional areas of the fluid tubes, or may be due to a change in the fluid density. Therefore, this approach is not very useful in the field when the fluid flowing through the vibrating meter may have an unknown or a changing density.
There are also numerous prior art examples that explain how to determine a fluid tube stiffness based on a vibrational response of the fluid tube. As mentioned above, the fluid tube stiffness is generally determined during an initial calibration and is required to accurately determine a flow calibration factor of the meter. In addition to the initial calibration methods that are well known in the art and widely utilized in the vibrating meter industry, other prior art examples attempt to determine the fluid tube stiffness in situ using the existing driver and pick-off arrangement. For example, U.S. Pat. No. 6,678,624, assigned on its face to the present applicants, discloses a method that determines a modal dynamic stiffness matrix and subsequently determines the fluid tube stiffness. U.S. Pat. No. 7,716,995, assigned on its face to the present applicants, discloses another prior art approach that utilizes two or more vibrational responses and solves a single degree of freedom differential equation to determine the fluid tube's stiffness, damping, and mass characteristics, among other characteristics of the vibrating meter. As discussed in the '995 patent, in the most basic explanation, vibration of the Coriolis meter can be characterized using a simple spring equation:
                              2          ⁢          π          ⁢                                          ⁢          f                =                                            2              ⁢              π                        τ                    =                                    k              m                                                          (        1        )            
Where:
f is the frequency of oscillation;
m is the mass of the assembly;
τ is the period of oscillation; and
k is the stiffness of the assembly.
Equation (1) can be rearranged to solve for the stiffness, k and the mass of the assembly can be easily measured using existing driver and pick-off assemblies.
Another prior art attempt at detecting changes in the cross-sectional areas of the fluid tubes is disclosed by U.S. Pat. No. 7,865,318, which is assigned on its face to the present applicants and is hereby incorporated by reference for all that it teaches. The '318 patent measures the stiffness of the fluid tubes based on a resonant drive frequency. The '318 patent explains that the vibrational response of a flow meter can be represented by an open loop, second order drive model, comprising:M{umlaut over (x)}+C{dot over (x)}+Kx=f  (2)
Where:
f is the force applied to the system;
x is the physical displacement of the fluid tube;
{dot over (x)} is the velocity of the fluid tube;
{umlaut over (x)} is the acceleration of the fluid tube;
M is the mass of the system;
C is the damping characteristic; and
K is the stiffness characteristic of the system.
The '318 patent performs a number of substitutions and eventually arrives at equation (3) (equation 9 in the '318 patent), which is outlined as follows:
                    K        =                              I            *                          BL              PO                        *                          BL              DR                        *                          ω              o                                            2            ⁢            ζ            ⁢                                                  ⁢            V                                              (        3        )            
Where:
ζ is the damping characteristic;
V is the drive voltage;
BLPO is the pick-off sensitivity factor;
BLDR is the driver sensitivity factor; and
I is the drive current.
The pick-off sensitivity factor and the driver sensitivity factor are generally known or measured for each pick-off sensor and driver. The damping characteristic is typically determined by allowing the vibrational response of the flow meter to decay down to a vibrational target while measuring the decay. Therefore, as explained in the '318 patent, the stiffness parameter (K) can be determined by measuring/quantifying the damping characteristics (ζ) the drive voltage (V); and the drive current (I). Although the approach proposed by the '318 patent can provide satisfactory results in certain situations, such as when changes in the drive mode stiffness occur, testing has shown that changes in the cross-sectional areas of curved fluid tubes, especially due to corrosion or erosion typically occurs in the outer radius of the tube bends, slightly downstream from the tube bends, or at the tube/manifold weld joints. While M, C, K, and ζ described above are mode dependent, the current methods measure the drive mode resonant frequency, ωo and M, C, K, and ζ, in the drive mode. The drive mode stiffness (K) is altered when the wall thickness of the fluid tubes is altered. However, because erosion generally results in changes in the bends, changes in these areas often have very little impact on the generally measured bend mode, which are vibrated in typical vibrating meters at the drive mode resonant frequency, ωo, discussed in the '318 patent, for example. In order to detect changes in the bends, stress/strain needs to be produced in the bends, which does not generally occur when driving the fluid tubes in the drive mode. Therefore, prior art meters cannot typically detect a change in the cross-sectional areas of the fluid tubes using the current driver and pick-off architecture.
It should be appreciated that determining the fluid tube's stiffness and damping characteristics is required for practically all vibrating meters. Consequently, although specific equations are provided above, they should in no way limit the scope of the embodiments described below. Those skilled in the art will readily recognize alternative equations and methods for determining fluid tube stiffness based on a measured vibrational response.
Due to the inadequate stiffness determinations currently available, there is a need in the art for a system that detects a possible change in the material and/or cross sectional properties of a fluid tube indicating the measurements provided by the vibrating meter may be inaccurate. The embodiments described below overcome these and other problems and an advance in the art is achieved. The embodiments described below provide a vibrating meter that can be vibrated in a lateral mode in addition to the typical drive mode (bend). Because the changes in cross-sectional area generally occur at the outer radius of the tube bends, the change in cross-sectional area will affect the lateral mode stiffness of the fluid tubes to a much greater extent than the drive mode stiffness. In other words, a change in the lateral mode stiffness will not have a significant effect on the drive mode vibrational frequency, but will often change the lateral mode vibrational resonant frequency.